Integrable two-channel p_x+ip_y-wave superfluid model

We present a new two-channel integrable model describing a system of spinless fermions interacting through a p-wave Feshbach resonance. Unlike the BCS-BEC crossover of the s-wave case, the p-wave model has a third order quantum phase transition. The critical point coincides with the deconfinement of a single molecule within a BEC of bound dipolar molecules. The exact many-body wavefunction provides a unique perspective of the quantum critical region suggesting that the size of the condensate wavefunction, that diverges logarithmically with the chemical potential, could be used as an experimental indicator of the phase transition.Comment: 4 pages, 4 figure

Approximated integrability of the Dicke model

A very approximate second integral of motion of the Dicke model is identified within a broad region above the ground state, and for a wide range of values of the external parameters. This second integral, obtained from a Born Oppenheimer approximation, classifies the whole regular part of the spectrum in bands labelled by its corresponding eigenvalues. Results obtained from this approximation are compared with exact numerical diagonalization for finite systems in the superradiant phase, obtaining a remarkable accord. The region of validity of our approach in the parameter space, which includes the resonant case, is unveiled. The energy range of validity goes from the ground state up to a certain upper energy where chaos sets in, and extends far beyond the range of applicability of a simple harmonic approximation around the minimal energy configuration. The upper energy validity limit increases for larger values of the coupling constant and the ratio between the level splitting and the frequency of the field. These results show that the Dicke model behaves like a two-degree of freedom integrable model for a wide range of energies and values of the external parameters.Comment: 6 pages, 3 figures. Second version with added text, references and some new figure

Exact solution of the spin-isospin proton-neutron pairing Hamiltonian

The exact solution of proton-neutron isoscalar-isovector (T=0,1) pairing Hamiltonian with non-degenerate single-particle orbits and equal pairing strengths (g_{T=1}= g_{T=0}) is presented for the first time. The Hamiltonian is a particular case of a family of integrable SO(8) Richardson-Gaudin (RG) models. The exact solution of the T=0,1 pairing Hamiltonian is reduced to a problem of 4 sets of coupled non linear equations that determine the spectral parameters of the complete set of eigenstates. The microscopic structure of individual eigenstates is analyzed in terms of evolution of the spectral parameters in the complex plane for system of A=80 nucleons. The spectroscopic trends of the exact solutions are discussed in terms of generalized rotations in isospace.Comment: 4 pages, 2 figure

Public policies for the Development of a Sustainable, Forage-Based Cattle Sector in Colombia, Argentina, and Costa Rica: A Comparative Analysis

Projected increases in global food demand highlight the importance of Latin America as one of the major future food suppliers, particularly regarding animal-source foods such as beef or milk. Despite the importance of the cattle sector for the region, its negative environmental impacts are numerous and the shift towards sustainability is perceived as slow and uncoordinated. This study aims to identify achievements and difficulties in the implementation of public policies for a sustainable cattle sector in Colombia, Argentina, and Costa Rica, for which policies focused on the use of silvo-pastoral systems and forage-based solutions are prioritized. Based on the review of scientific articles, government reports, and publications of international organizations, a comparative qualitative analysis was carried out, documenting the policy developments between 2010-2020. For the three countries, the findings highlight a large number of public policies focused on the implementation of silvo-pastoral systems, both at the local and national levels. At the same time, the efforts of the governments to include such strategies in the National Development Plans and stimulate legislative advances are evident. However, they also coincide in difficulties, such as the disconnection and lack of continuity between policies, unclear budgets for their financing, and little socialization within the communities. Another obstacle to the success of public policies is the way in which they are perceived by producers, who on many occasions refuse to make the transition from conventional to sustainable methods, considering that it implies the availability of economic resources, knowledge, and training that are difficult to access. The results also indicate that, despite the initiatives developed over the last ten years, problems such as deforestation and increasing greenhouse gas emissions persist in the three countries, although to different extents and at different levels. It is concluded that the policy efforts for the implementation of silvo-pastoral systems should be seen as initial steps in a long-term process towards achieving a sustainable cattle sector. Recommendations are provided that could help increase the success of these and new policies at different stages, from the identification of the problem to their evaluation, particularly given the difficulties of financing, disconnection, and participation of citizens and producers